A mechanistic modelling and data assimilation approach to estimate the carbon/chlorophyll and carbon/nitrogen ratios in a coupled hydrodynamical-biological model

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in Geophysics

A mechanistic modelling and data assimilation approach to estimate

the carbon/chlorophyll and carbon/nitrogen ratios in a coupled

hydrodynamical-biological model

B. Faugeras1, O. Bernard2, A. Sciandra3, and M. Lévy4 1_{Institut de Recherche pour le Développement (IRD), Sète, France}

2_{Institut National de Recherche en Informatique et Automatique (INRIA), COMORE project, Sophia-Antipolis, France} 3_{Laboratoire d’Oc´eanographie de Villefranche-sur-mer (LOV), CNRS, Villefranche-sur-mer, France}

4_{Laboratoire d’Oc´eanographie Dynamique et de Climatologie (LODYC), CNRS, Paris, France}

Received: 19 July 2004 – Revised: 6 November 2004 – Accepted: 8 November 2004 – Published: 12 November 2004

Abstract. The principal objective of hydrodynamical-biological models is to provide estimates of the main carbon fluxes such as total and export oceanic production. These models are nitrogen based, that is to say that the variables are expressed in terms of their nitrogen content. Moreover models are calibrated using chlorophyll data sets. Therefore carbon to chlorophyll (C:Chl) and carbon to nitrogen (C:N) ratios have to be assumed. This paper addresses the prob-lem of the representation of these ratios. In a 1D framework at the DYFAMED station (NW Mediterranean Sea) we pro-pose a model which enables the estimation of the basic bio-geochemical fluxes and in which the spatio-temporal vari-ability of the C:Chl and C:N ratios is fully represented in a mechanical way. This is achieved through the introduc-tion of new state variables coming from the embedding of a phytoplankton growth model in a more classical Redfieldian NNPZD-DOM model (in which the C:N ratio is assumed to be a constant). Following this modelling step, the parameters of the model are estimated using the adjoint data assimilation method which enables the assimilation of chlorophyll and ni-trate data sets collected at DYFAMED in 1997.

Comparing the predictions of the new Mechanistic model with those of the classical Redfieldian NNPZD-DOM model which was calibrated with the same data sets, we find that both models reproduce the reference data in a comparable manner. Both fluxes and stocks can be equally well pre-dicted by either model. However if the models are coincid-ing on an average basis, they are divergcoincid-ing from a variability prediction point of view. In the Mechanistic model biology adapts much faster to its environment giving rise to higher short term variations. Moreover the seasonal variability in total production differs from the Redfieldian NNPZD-DOM model to the Mechanistic model. In summer the Mechanistic Correspondence to: B. Faugeras

([email protected])

model predicts higher production values in carbon unit than the Redfieldian NNPZD-DOM model. In winter the contrary holds.

1 Introduction

The estimation of the amount of carbon fixed by oceanic phy-toplankton during primary production is a key point to quan-tify the future evolution of atmospheric carbon. To address this issue biogeochemical models are increasingly being used and applied to a variety of regions in the ocean. Most of these models are more or less complex variants of the Fasham et al. (1990) model and are nitrogen based. That is to say that the compartments or state variables of the model, and in partic-ular phytoplankton, are expressed in terms of their nitrogen content (mmolN/m3). The main reason for this is that ni-trogen plays a critical role in ocean biology as an important limiting nutrient in a wide range of areas. Therefore it is a natural currency for modelling biological fluxes.

However, if the aim of such a model is to estimate and pre-dict carbon fluxes, then carbon to nitrogen ratios have to be assumed. It is therefore quite common to use the Redfield ratio to convert the nitrogen fluxes computed from the phy-toplankton compartment to carbon fluxes. However the ni-trogen to carbon ratio is known to be highly variable (Droop, 1968; Bury et al., 2001) both in time and space.

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0 250 500

0 10 20 30 40

Time (days)

Particulate carbon (µM C)

d=0 d=0.3 d=0.1

0 20 40 60 80 100 120

0 10 20 30 40

Time (days)

Chlorophyll a (µg.L

-1 )

d=0 d=0.3 d=0.1

Fig. 1. Comparison of experimental data in chemostat with Rhodomonas salina (Cryptophyceae) and the BIOLOV model output for particular

carbon (left) and chlorophyll (right). The dilution rate is successively set to 0, 0.3 and 0.1 d−1. From Pawlowski et al. (2002).

to be constant (Fasham et al., 1990), and in more detailed approaches it can be represented as a static function of light and nitrogen (Doney et al., 1996; L´evy et al., 1998). From laboratory studies it was demonstrated that the C:Chl is also highly variable, especially in conditions of nitrogen limita-tion (Rhee and Gothan, 1981; Sciandra et al., 1997). In the end, the biochemical models which take explicitly into ac-count the physiological plasticity of the phytoplankton are rather scarce (Lefevre et al., 2003).

Then the main question that we want to address in this pa-per rises. What are the effect of the variability of the C:N and C:Chl ratio on the predictions of the biogeochemical models and on their calibration? What is the benefit of complexi-fying the model by predicting these ratio with a Mechanistic model integrating the phenomenon of coupling between light and nitrogen limitation?

The goal of this paper is to address this aspect using a cou-pled hydrodynamical-biological modelling. This work fol-lows another study where only the spatial variability of the C:Chl was considered (Faugeras et al., 2003), and was es-timated through an assimilation step. Here we consider the same 1D framework at the DYFAMED station, we propose a model which enables the estimation of the basic biogeo-chemical fluxes and in which the spatio-temporal variability of the C:Chl and C:N ratios is fully represented in a mechan-ical way.

This is achieved through the use of a new biological model (the BIOLOV model Pawlowski et al., 2002; Pawlowski, 2004)) developed and validated in chemostat experiments. This phytoplanktonic model describes independently the be-haviour of phytoplanktonic carbonC, nitrogenNand chloro-phyllL. It is an alternative to other existing models, like the model presented in Geider et al. (1997) or in Baumert (1996). Note that other more complicated phytoplankton growth models predicting the behaviour of these variables could be used (Zonneveld, 1998; Flynn, 2001), but their higher complexity make them much more difficult to inte-grate in the framework of a biogeochemical model. Figure 1 demonstrates the ability of the BIOLOV model to reproduce, with a limited set of parameters, both the steady state

val-ues and the transients for chemostat experiments with the Cryptophyceae Rhodomonas salina. The considered cou-pled hydrodynamical-biological model thus results from the embedding of this BIOLOV phytoplankton growth model, in a 1D Redfieldian NNPZD-DOM model (Nitrate, Ammo-nium, Phytoplankton, Zooplankton Detritus, Dissolved Or-ganic Matter) already validated at DYFAMED under con-stant and fluctuating experimental conditions.

The objective of this paper is not to fully compare this “classical” 1D Redfieldian NNPZD-DOM model with our new model in terms of the quality of the simulated most im-portant biogeochemical fluxes such as production and export. Actually this would have been an interesting question to ad-dress but as shown in Faugeras et al. (2003) production and export fluxes estimates can not be recovered at DYFAMED from stock (chlorophyll and nitrate) data. Indeed they have shown that some measurements of these fluxes need to be in-cluded in the assimilation process in order to constrain pa-rameter estimation and to guaranty consistent predictions. As a consequence both models produce comparable average fluxes values since these are constrained by data assimilation. Therefore we clearly concentrate on the spatial and temporal variability of the fluxes and ratios as predicted by the mod-els. Then we estimate the benefit of using more complicated models if we want to account both the average value and the variability of these quantities.

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depth (m) Deg C 04/12 -300 -250 -200 -150 -100 -50 0

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depth (m)

Deg C 04/12

Fig. 2. Temperature profiles. Model results vs. data collected at DYFAMED in 1997; solid line: data; dashed line: simulation.

relatively well known (Deep-Sea Res. II, special issue, 49, 11, 2002), and has been the subject of previous model stud-ies (L´evy et al., 1998; M´emery et al., 2002; Faugeras et al., 2003).

The paper is organized as follows: Sect. 2 is devoted to the construction of the new model by embedding the BIOLOV model into the 1D Redfieldian NNPZD-DOM model. In all this paper the Redfieldian NNPZD-DOM model is also sim-ply referred to as “the Redfieldian model” or “the NNPZD-DOM model”, and the new proposed model is referred to as “the Mechanistic model”.

Section 3 discusses the calibration of the Mechanistic model using data assimilation. Numerical results are pre-sented in Sect. 4 and a Discussion section ends the paper.

2 Model presentation

2.1 A one-dimensional NNPZD-DOM model

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N O3

DOM mortalitymzZ2

winter convection organic exudation

remineralization

µdomDOM remineralization _{N H} nitrification

4 _µ

nN H4

grazing

GdD

fecal pellets

breakdown

(1−fn)µdD

vd

∂D ∂z

sedimentation

organic exudation

(1−fn)µzZ fnµdD

D +(1−ad)GdD

mortality

fnµzZ inorganic exudation

P

GpP

(1−ap)GpP

mpP

fnγµpLI(LN O3+LN H4)P

(1−fn)γµpLI(LN O3+LN H4)P

regenerated production

µpLILN H4P

new production

µpLILN O3P

Z

grazing

Fig. 3. Schematic representation of the compartments and processes of the NNPZD-DOM surface layer model.

number of prognostic variables. Nitrate and ammonium al-low the estimation of new and regenerated production, zoo-plankton mortality and detrital sedimentation feed the parti-cle export flux.

The biological model is embedded in a 1D physical model, which simulates the evolution over time of velocity, temper-ature, salinity and turbulent kinetic energy (TKE). Figure 2 shows temperature profiles (simulated profiles versus data which were used to calibrate the physical model). As for dy-namical processes, the only one taken into account is vertical diffusion. The mixing coefficient,K, is obtained diagnosti-cally from TKE, with a 1.5 closure scheme in the Mellor Ya-mada nomenclature (Gaspar et al., 1990). The model covers the first 400 m of the water column, with a vertical discretiza-tion of 5 m.

Biological tracers are vertically mixed with the same dif-fusion coefficient as temperature and salinity. A specific bi-ological reaction term, FB, is added to the diffusion

equa-tion. Tracers are expressed in terms of their nitrogen contents (mmolNm−3). For each of the state variables, NO3, NH4,P,

Z,DandDOM, the prognostic equation reads as follows:

∂B

∂t −

∂

∂z(K

∂B

∂z)=FB, (1)

whereB is one of the state variables i.e. one of the biolog-ical tracer concentration. A schematic representation of the model is shown on Fig. 3 and the parameters are presented in Table 1.

The formulation of phytoplankton growth takes into ac-count limitation by both nutrients and light. Following Hurtt and Armstrong (1996), a Michaelis-Menten function,LNH4,

is used to express limitation by ammonium:

LNH4 =

NH4

kn+NH4

. (2)

Based on the hypothesis that the total limitation, by both am-monium and nitrate,LNO3 +LNH4, follows the same law,

-200 -150 -100 -50 0

33 44 55 66 77 88 99 110 121 132 143 154 165

depth (m)

C/Chl ratio (mgC/mgChl) -200

-150 -100 -50 0

33 44 55 66 77 88 99 110 121 132 143 154 165

depth (m)

C/Chl ratio (mgC/mgChl)

Fig. 4. Dashed line: first guess constant C:Chl ratio. Continuous line: C:Chl ratio allowing vertical variability estimated through the assimilation of the 1997 DYFAMED data set (from Faugeras et al., 2003). Also see Fig. 12 for a plot of this ratio as a function of light.

i.e.

LNO3+LNH4 =

NO3+NH4

(kn+NO3+NH4)

, (3)

we obtain for the expression of limitation by nitrate,

LNO3 =

knNO3

(kn+NH4)(kn+NO3+NH4)

. (4)

The function, LI, representing limitation by light is

ex-pressed as follows:

LI =1−exp(−I (z, P )/ kpar). (5)

The photosynthetic available radiation,I (z, P ), is predicted from surface irradiance and phytoplankton pigment content according to a simplified version of a light absorption model detailed in Morel (1988). Two different wavelengths corre-sponding to green and red are considered and the associated absorption coefficients,kg andkr, depend on the local

phy-toplankton concentrations:

kg=kgo+kgp(

12P rd rpigrc

(5)

Table 1. The 28 parameters of the NNPZD-DOM model (excluding the 20 parameters of the C:Chl profile).

parameter name value unit

half-saturation const. for nutrients kn 0.01 mmolN.m−3

carbon/chlorophyll ratio rc 55 mgC.mgChla−1

phyto. exudation fraction γ 0.05

zoo. nominal preference for phyto food r 0.7

max. specific zoo. grazing rate gz 8.68E-6 s−1

half-saturation const. for grazing kz 1 mmolN.m−3

non-assimilated phyto. by zoo. ap 0.3

non-assimilated detritus by zoo. ad 0.5

zoo. specific exudation rate µz 1.16E-6 s−1

phyto. mortality rate mp 9.027E-7 s−1

zoo. mortality rate mz 1.0E-7 mmolN.m−3.s−1

detritus breakdown rate µd 1.04E-6 s−1

detritus sedimentation speed vd 5.8E-5 m.s−1

max. phyto. growth rate µp 2.31E-5 s−1

light half-saturation const. kpr 33.33 W.m−2

decay rate below the euphotic layer τ 5.80E-5 s−1

ratio of inorganic exudation fn 0.8

nitrification rate µn 3.81E-7 s−1

slow remineral. rate ofDOMto NH₄ µ_dm 6.43E-8 s−1

coeff. for Martin’s remineralization profile hr −0.858

pigment absorption in red krp 0.037 m−1.(mgChl.m−3)−lr

pigment absorption in green kgp 0.074 m−1.(mgChl.m−3)−lg

power law for absorption in red lr 0.629

power law for absorption in green lg 0.674

contribution of Chl to absorbing pigments r_pig 0.7

water absorption in green kgo 0.0232 m−1

water absorption in red kro 0.225 m−1

carbon/nitrogen ratio rd 6.625 mmolC.mmolN−1

kr =kro+krp(

12P rd rpigrc

)lr_. ₍₇₎

ThenI (z, P )is written as the sum of the contribution from

each of the two considered wave lengths:

I (z, P )₌Ir(z, P )+Ig(z, P ). (8)

Given an initial condition on the surface, I (z₌0) propor-tional to the solar flux and split equally into

Ig(z=0)=Ir(z=0)=I (z=0)/2, (9)

Ir(z, P )andIg(z, P )are computed recursively according to

the following absorption equations:

Ig(z, P )=Ig(z−1z, P )(1−exp(−kg1z)), (10)

Ir(z, P )=Ir(z−1z, P )(1−exp(−kr1z)), (11)

where1zis the space discretization step along the water col-umn.

Grazing of phytoplankton and detritus is formulated fol-lowing Fasham et al. (1990):

Gp=Gp(P , Z, D)=

gzrP Z

kz(rP+(1−r)D)+rP2+(1−r)D2

, (12)

Gd=Gd(P , Z, D)=

gz(1−r)DZ

kz(rP+(1−r)D)+rP2+(1−r)D2 .(13) Other modelled biogeochemical interactions include phyto-plankton mortality, phytophyto-plankton exudation, zoophyto-plankton mortality (considered as large particles which are supposed to be instantaneously exported below the productive layer and remineralized in the water column), zooplankton exuda-tion, fecal pellet producexuda-tion, detritus sedimentaexuda-tion, detritus breakdown, nitrification, and dissolved organic matter rem-ineralization (Fig. 3).

Below a depth of 150 m, remineralization processes are preponderant and the surface model does not apply. Instead, decay of phytoplankton, zooplankton and detritus in nutri-ents with a rateτ, and a vertical redistribution of zooplankton mortality according to Martin’s profile (Martin and Fitzwa-ter, 1992) parameterize remineralization below the surface layer. This parameterization conserves total nitrogen.

An important point in the formulation of this NNPZD-DOM model concerns the C:Chl ratio, rc. It is a

parame-ter which enparame-ters the model through the light limitation parame-term

LI (Eqs. 6 and 7). It is used to convert phytoplankton P

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C photosynthesis

a(I)L

respiration

λC

ρm

S

S+KS

C

U L

S

synthesis

γ(I)UL

C

βL

degradation uptake

Fig. 5. Schematic representation of the compartments and processes of the BIOLOV model.

choose rc is to take a constant (in space and time) value.

However as with earlier studies, (Geider et al., 1997), it is quantitatively shown in Faugeras et al. (2003) assimilating data from the DYFAMED station that it is impossible to sim-ulate a correct surface chlorophyll bloom intensity together with a correct summer subsurface chlorophyll maximum in an oligotrophic regime using this constant C:Chl ratio. This is also in agreement with experimental observations show-ing a large increase of the C:Chl ratio with respect to light (Cullen, 1990; Chalup and Laws, 1990). To overcome this difficulty the authors gave a vertical variability to this ratio (Fig. 4). This lead to a significant improvement of the data assimilation results. However this is expensive from a com-putational point of view since a function of depth involving 20 parameters has to be estimated instead of a single param-eter. Moreover the obtained profile of C:Chl ratio is strongly site dependent and extrapolation of the model to other areas is therefore delicate. Some other studies (Doney et al., 1996; L´evy et al., 1998) propose to parameterize the C:Chl ratio as a static function of light in the water column. It is therefore varying in space and time. Here we propose a mechanical and more realistic representation of the dynamical variations of the C:Chl ratio with respect to environmental conditions. The main tool we use to achieve this objective is the BIOLOV model presented in the following section.

2.2 The BIOLOV model

Modelling growth of phytoplankton both limited by light and nitrogen has been an active research field in the previous years. It resulted in several models of various complexity. Some works describe with much details the involved mech-anisms of coupling between carbon and nitrogen assimila-tion, resulting in complex models where many state vari-ables are necessary to describe phytoplankton growth (Zon-neveld, 1998; Flynn, 2001). These models are less con-venient to integrate in a biogeochemical framework since they considerably increase the computational cost. More-over the calibration of such models becomes a critic issue since the large number of parameters to be estimated may jeopardize the classical assimilation techniques. On the other hand there exists simpler models that focus on the main vari-ables of interest: total cellular carbon, nitrogen and chloro-phyll (Baumert, 1996; Geider et al., 1997). The application of these models have so far been limited to balanced growth

N H₄ N O₃

DOM

GpU grazing

grazing mortalitymzZ2

winter convection ammonium

uptake ρ(I)LN H4C

organic exudation inorganic exudation

(1−fn)γρ(I)(LN O3+LN H4)C

remineralization µdomDOM

remineralization nitrification µnN H4

synthesis

grazing GdD

fecal pellets

breakdown (1−fn)µdD

vd

∂D ∂z sedimentation

organic exudation (1−fn)µzZ

fnµdD

GpL

degradation

GpC mpC

photosynthesis a(I)L

respiration λC

nitrate uptake ρ(I)LN O3C Z

L

U

C

D

γ(I)UL C

(1−ap)Gp(U+L) +(1−ad)GdD

βL

grazing mortality

mortality mpU mortality

mpL

fnµzZ fnγρ(I)(LN O3+LN H4)C

Fig. 6. Schematic representation of the compartments and processes of the new model.

conditions for which they have been validated. The BIOLOV model (Pawlowski et al., 2002) is a phytoplankton growth model which was developed and validated in chemostat ex-periments, under unbalanced growth conditions (see Fig. 1). In the BIOLOV model phytoplankton is represented by 3 variables: the carbon C, the non-chlorophyllian nitrogen

U and the chlorophyllian nitrogenL. It was originally for-mulated for a chemostat as a system of ordinary differen-tial equations describing the evolution of 4 state variablesC

(expressed in mmolC.m−3),U, LandS, the nitrogen source (expressed in mmolN.m−3). Letf (mmolN.mmol Chla−1) denote the conversion factor from chlorophyllian nitrogen to chlorophylla(see Table 3): Chl=f L. The model integrates both limitation by light and nitrogen and has been designed to have a simple formulation with few parameters and state variables representing measurable quantities in a photobiore-actor or in the open ocean. Figure 5 shows a schematic rep-resentation of the model and its parameters are presented in Table 2.

Phytoplankton growth is assumed to be triggered by two distinct metabolic pathways: uptake and assimilation of ni-trogen on one hand and carbon fixation through photosynthe-sis on the other hand.

The full nitrogen pathway consists in three steps. First ni-trogen (S) is uptaken by the cell into the cellular nitrogen pool (U). The uptake rate is classically represented by a Monod kinetics,

ρm S

KS+S

. (14)

In a second step, the nitrogen pool is used to produce chloro-phyllian proteins (L). The chlorophyll synthesis is assumed to be dependent on light intensity,I, and on the ratio L

C. It

is also proportional to the nitrogen poolU. The rate of the reaction is therefore assumed to be given byγ (I )UL

C where

γ (I )₌ αKLI

KI +I

KC

KC+I

(7)

Table 2. Parameters of the BIOLOV model.

max. assimilation rate ρm 5.787 E-6 mmolN.mmolC−1.s−1

half-saturation const. for assimilation KS 0.43 mmolN m−3

max. Chl synthesis rate KL 6.59

Chl. synthesis threshold coefficient KC 33.0 µmol quanta.m−2.s−1

max. fixation rate for carbon α 2.7894 E-4 s−1

half-saturation const. for carbon fixation KI 208.5 µmol quanta.m−2.s−1

respiration rate λ 6.25 E-7 s−1

Chl. degradation rate β 3.9931 E-6 s−1

Finally, a natural degradation of chlorophyll is also taken into account through a rateβL.

The carbon pathway results from two reactions. First, in-organic carbon (DI CDissolved Inorganic Carbon) is incor-porated into the cell through photosynthesis to form particu-late carbon,C.

For sake of simplicity we assume a constant quantum yield, resulting thus in the photosynthesis rate per carbon unit

a(I )L/Cwith

a(I )₌ αI

KI+I

. (16)

This rate is highly dependent on light level and chlorophyll pigments which act as catalyzers for this reaction. This very simple expression compared to the one used e.g. by (Gei-der et al., 1997) allows to keep the model simple avoiding additional parameters that may limit the efficiency of the as-similation procedure.

Inorganic carbon is considered as non-limiting for phyto-plankton growth in marine environment and therefore it does not intervene. Second, a proportion of the carbon is lost by respiration. The respiration rate is proportional to the carbon biomass and is writtenλC.

2.3 Combining the 1D NNPZD-DOM model and the BI-OLOV model

Now that we have briefly described the 1D NNPZD-DOM model and the BIOLOV model we are able to construct our new model. Our goal is to embed the BIOLOV model into the NNPZD-DOM model, in order to obtain a model which can be compared to the DYFAMED data set and in which the carbon/chlorophyll ratio evolves dynamically. In line with our objective to compare the effect of different phyto-plankton parametrization on prediction variability we kept unchanged the hydrodynamical model as well as the other compartments of the biological model.

Phytoplankton is not anymore represented by a single vari-ableP but by the 3 variablesU, LandC. Figure 6 shows a complete representation of the compartments and processes of the new model, and all parameters are presented in Table 3. The different reaction terms can now be written as follows.

FNO3 = −ρp(I )LNO3C+µnNH4, (17)

0 1 2 3 4 5 6

0 50 100 150 200 250 300 350

mgChla/m3

days

Mechanistic model first guess Mechanistic model assimilated run Redfieldian model surface data profile data

Fig. 7. Surface chlorophyll (mgChla/m3) computed with the

Mech-anistic model (first guess and assimilated run) and with the Red-fieldian model. Crosses are the surface observations. Squares are the surface measurements taken from the chlorophyll profile set (Fig. 8).

FNH4 = −ρp(I )LNH4C+fnγρp(I )(LNO3+LNH4)C

+fnµzZ+fnµdD−µnNH4+µdomDOM, (18)

FU =ρp(I )LNO3C+ρp(I )LNH4C−fnγρp(I )(LNO3+LNH4)C

−(1₋fn)γρp(I )(LNO3+LNH4)C−γ (I )U L

C+βL

−Gp(U+L, D, Z)U−mpU,

(19)

FL=γ (I )U

L

C −βL−mpL−Gp(U+L, D, Z)L, (20)

FC =a(I )L−λC−mpC−Gp(U+L, D, Z)C, (21)

FZ =Gp(U+L, D, Z)(U+L)+Gd(U+L, D, Z)D

−(1₋ad)Gd(U+L, D, Z)D

−(1₋ap)Gp(U+L, D, Z)(U+L)−mzZ2−µzZ,

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FD=(1−ap)Gp(U+L, D, Z)(U+L)

+(1₋ad)Gd(U+L, D, Z)D

−Gd(U+L, D, Z)D+mp(U+L)

−fnµdD−(1−fn)µdD−vd ∂D

∂z,

(8)

Table 3. 33 parameters of the Mechanistic model.

half-saturation const. for nutrients kn 0.3208 mmolN m−3

phyto. exudation fraction γ 0.0649

zoo. nominal preference for phyto food r 0.6279

max. specific zoo. grazing rate gz 1.2152E-5 s−1

half-saturation const. for grazing kz 1.291 mmolN.m−3

non-assimilated phyto. by zoo. ap 0.333

non-assimilated detritus by zoo. ad 0.555

zoo. specific exudation rate µz 8.120E-7 s−1

phyto. mortality rate mp 1.354E-6 s−1

zoo. mortality rate mz 1.058E-7 mmolN.m−3.s−1

detritus breakdown rate µd 1.352E-6 s−1

detritus sedimentation speed vd 4.1122E-5 m.s−1

decay rate below the euphotic layer τ 5.5738E-5 s−1

ratio of inorganic exudation fn 0.7488

nitrification rate µn 3.0213E-7 s−1

slow remineral. rate ofDOMto NH4 µdm 4.8675E-8 s−1

coeff. for Martin’s remineralization profile hr -0.858

pigment absorption in red krp 0.037 m−1.(mgChl.m−3)−lr

pigment absorption in green kgp 0.074 m−1.(mgChl.m−3)−lg

power law for absorption in red lr 0.629

power law for absorption in green lg 0.674

contribution of Chl to absorbing pigments rpig 0.7

water absorptions in green kgo 0.0232 m−1

water absorptions in red kro 0.225 m−1

max. assimilation rate ρm 8.6805E-6 mmolN.mmolC−1.s−1

light half-saturation const. for assimilation KI2 104.25 µmol quanta.m−2.s−1

Chl. synthesis threshold coefficient KC 33.0 µmol quanta.m−2.s−1

max. fixation rate for carbon α 2.7894 E-4 s−1

max. Chl. synthesis rate αK 1.800E-3 s−1

half-saturation const. for carbon fixation K_I 208.5 µmol quanta.m−2.s−1

respiration rate λ 6.25 E-7 s−1

Chl. degradation rate β 7.9862 E-7 s−1

L/Chl ratio f 0.43 mmolN.m−3/mgChl.m−3

FDOM =(1−fn)γρp(I )(LNO3+LNH4)C

+(1₋fn)µzZ+(1−fn)µdD−µdomDOM, (24)

where

Gp=Gp(U+L, D, Z), (25)

and

Gd=Gd(U+L, D, Z). (26)

Let us make a few comments on some important modelled processes:

– nutrient uptake:

Contrary to the BIOLOV model not only nitrate but also ammonium is represented in the model. However the uptake rate still uses a Monod kinetics as in the BI-OLOV model (henceS₌NO3+NH4),

LNO3 +LNH4 =

NO3+NH4

kn+NO3+NH4

.

Concerning the BIOLOV model the new variableC ap-pears in the formulation of the uptake rate,

ρp(I )(LNO3 +LNH4)C.

However in the simplest version of the BIOLOV model the maximum uptake rate is a constant,ρm, and the

up-take rate does not depend explicitly on light. Numeri-cal sensitivity studies reinforced by light dark chemo-stat experiments suggested that this is a too raw approx-imation in our 1D DYFAMED context. We therefore choose to allow light dependence of the maximum up-take rate through the following formulation:

ρp(I )= ρmI KI2+I

.

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-200 -150 -100 -50 0

0 0.5 1 1.5 2

01/13 depth (m) mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

01/13 depth (m) mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

01/13 depth (m) mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

01/13 depth (m) mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

02/23 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

02/23 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

02/23 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

02/23 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/02 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/02 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/02 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/02 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/21 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/21 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/21 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

03/21 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

04/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

04/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

04/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

04/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

05/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

05/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

05/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

05/15 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

06/19 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

06/19 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

06/19 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

06/19 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

07/12 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

07/12 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

07/12 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

07/12 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

09/01 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

09/01 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

09/01 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

09/01 mgChl/m3 -200 -150 -100 -50 0

0 0.5 1 1.5 2

11/18 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

11/18 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

11/18 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

11/18 mgChl/m3 depth (m) -200 -150 -100 -50 0

0 0.5 1 1.5 2

12/04 mgChl/m3 data -200 -150 -100 -50 0

0 0.5 1 1.5 2

12/04

mgChl/m3

data Mech. model first guess

-200 -150 -100 -50 0

0 0.5 1 1.5 2

12/04

mgChl/m3

data Mech. model first guess Mech. model assimil. run

-200 -150 -100 -50 0

0 0.5 1 1.5 2

12/04

mgChl/m3

data Mech. model first guess Mech. model assimil. run Redfieldian model

Fig. 8. Chlorophyll profiles (mgChla/m3) computed with the Mechanistic model (first guess and assimilated run) and with the Redfieldian

model. Depth in meters.

– Phytoplankton mortality and zooplankton grazing:

Phytoplankton mortality appears in the 3 equations for

U, Land C. The mortality rate, mp, is the same for

each of these variables.

In the same way, zooplankton grazing on phytoplankton now appears in each of the 3 equations forU, LandC. The grazing rateGp(U+L, D, Z)is the same for each

of these variables (U ₊Lrepresents total phytoplank-tonic nitrogen).

The carbon/chlorophyll ratio in mgC.mg Chla−1 (com-puted as 12fC_L) is now a diagnostic variable of the model and evolves dynamically in space and time. Chlorophyll data can be directly compared to the variable f L of the model, whereas in former studies phytoplankton and chloro-phyll were related through a linear relation,12P rd

rc (whererd

is the C:N ratio andrc the C:Chl ratio), in which the poorly

known C:Chl ratio played a crucial role.

3 Calibration of the new model using data assimilation

3.1 The DYFAMED data set

The model general set up is the same as in M´emery et al. (2002) and Faugeras et al. (2003). The standard run consists of the simulation of year 1997. The simulation is forced with ECMWF atmospheric data, which give the wind stresses and heat fluxes every 6 h.

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-200 -150 -100 -50 0

0 2 4 6 8

03/22 mmolN/m3 depth (m) -200 -150 -100 -50 0

0 2 4 6 8

03/22 mmolN/m3 depth (m) -200 -150 -100 -50 0

0 2 4 6 8

03/22 mmolN/m3 depth (m) -200 -150 -100 -50 0

0 2 4 6 8

03/22 mmolN/m3 depth (m) -200 -150 -100 -50 0

0 2 4 6 8

04/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

04/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

04/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

04/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

05/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

05/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

05/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

05/15 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

06/19 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

06/19 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

06/19 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

06/19 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

07/12 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

07/12 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

07/12 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

07/12 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

09/01 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

09/01 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

09/01 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

09/01 mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

10/18 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

10/18 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

10/18 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

10/18 depth (m) mmolN/m3 -200 -150 -100 -50 0

0 2 4 6 8

12/04 mmolN/m3 data -200 -150 -100 -50 0

0 2 4 6 8

12/04

mmolN/m3

data Mech. model first guess

-200 -150 -100 -50 0

0 2 4 6 8

12/04

mmolN/m3

data Mech. model first guess Mech. model assimil. run

-200 -150 -100 -50 0

0 2 4 6 8

12/04

mmolN/m3

data Mech. model first guess Mech. model assimil. run Redfieldian model

Fig. 9. NO₃profiles (mmolN/m3) computed with the Mechanistic model (first guess and assimilated run) and with the Redfieldian model.

Depth in meters.

in 1997 (Figs. 7, 8, 9). Following the conclusions of Faugeras et al. (2003) concerning the necessity to use flux and zoo-plankton data in the parameter estimation process, we also make use of annual estimates of total production (TP), nitrate uptake (NU) and export fluxes (EF, estimated from disparate measurements undertaken in the 90s), and of the zooplank-ton content estimated during a special cruise in May 1995 (Andersen and Prieur, 2000).

3.2 Parameter estimation

The purpose of parameter estimation is to find a set of op-timal parameters that minimises a cost function, J, which measures the distance, in a weighted least-squares sense, be-tween the model’s solution and the observations. The op-timisation is carried out using the quasi-Newton algorithm implemented in then1qn3 Fortran subroutine of Gilbert and Lemar´echal (1989). The computation of the gradient ofJ

with respect to control parameters is required at each step of the minimisation. This gradient results in one integration of the adjoint model. The adjoint code was partially obtained using the automatic differentiation program Odyss´ee (Faure and Papegay, 1997; Griewank, 2000), which is an efficient tool for obtaining adjoint codes since it enables the automatic production of adjoint instructions. This so called variational

adjoint method has already been applied in marine biogeo-chemistry by several authors (see Lawson et al., 1995, for example).

As shown in Table 3, the biological parameters have very different orders of magnitude. To avoid any numerical diffi-culties which might arise from this during the minimization, we adimensionalise the parameter vectorK, dividing each parameterKi by its first guess valueKi0,ki =Ki/Ki0. Such

a non-dimensionalisation procedure can be regarded as a pre-conditioning for minimization. The control variable iskof sizep, wherepis the number of parameters, andkis dimen-sionless.

The model-data misfit part,J0, of the cost function can be

written as the sum of five terms:

J0(k)=Jsc(k)+Jcp(k)+Jnp(k)+Jzoo(k)+Jflux(k).

Letd denote the data andφthe operator which, to a set of parameterk, associates the equivalents to the data computed by the model, φ (k). ThenJsc, the cost related to the nsc

surface chlorophyll observations,dscreads:

Jsc(k)=

1 2

ncs X

i=1

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-200 -150 -100 -50 0

0 50 100 150 200 250

01/13 depth (m) mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

01/13 depth (m) mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

01/13 depth (m) mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

01/13 depth (m) mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

02/23 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

02/23 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

02/23 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

02/23 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

03/02 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

03/02 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

03/02 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

03/02 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 03/21 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 03/21 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 03/21 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 03/21 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

04/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

04/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

04/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

04/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

05/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

05/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

05/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

05/15 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 06/19 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 06/19 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 06/19 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 06/19 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

07/12 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

07/12 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

07/12 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

07/12 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

09/01 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

09/01 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

09/01 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

09/01 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 11/18 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 11/18 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 11/18 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

depth (m) 11/18 mgC/mgChl -200 -150 -100 -50 0

0 50 100 150 200 250

12/04 mgC/mgChl first guess -200 -150 -100 -50 0

0 50 100 150 200 250

12/04 mgC/mgChl first guess assimilated run -200 -150 -100 -50 0

0 50 100 150 200 250

12/04 mgC/mgChl first guess assimilated run -200 -150 -100 -50 0

0 50 100 150 200 250

12/04

mgC/mgChl

first guess assimilated run

Fig. 10. Mean carbon to chlorophyll ratio profiles for year 1997 at DYFAMED. Thin dashed lines indicate that the algal biomass is very weak, and thus that the ratio is computed with very small values of C or Chl.

Jcpis related to thencpchlorophyll profile observations,dcp

(mcpmeasurement points on the vertical),

Jcp(k)=

1 2

ncp X

i=1

mcp X

l=1

wcp(φcp(k)i,l−dcpi,l)2.

Jnpis related to thennpNO3profile observations,dnp(mnp

measurement points on the vertical),

Jnp(k)=

1 2

nnp X

i=1

mnp X

l=1

wnp(φnp(k)i,l−dnpi,l)2.

Jzoois related to the single zooplankton data,

Jzoo(k)=

wzoo

2 (φzoo(k)−dzoo)

2_.

Jfluxis related to the TP, NU and EF data estimates.

Jflux(k)=

wtp

2 (φtp(k)−dtp)

2

+w₂nu(φnu(k)−dnu)2+

wef

2 (φef(k)−def )

2_.

The different weightsware composed of the square of the assumed a priori observation errors and of a scaling factor ac-counting for the number of each type of observation. There-fore, we havewcs =

1

ncs.σ2

cs

,wcp =

1

(ncp.mcp)σ2

cp

, and

wnp=

1

(nnp.mnp)σ2

np

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-200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 01/13 depth (m) mgC/mgN -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN 02/23 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN 03/02 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 03/21 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 03/21 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 03/21 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 03/21 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN 04/15 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN 05/15 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 06/19 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 06/19 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 06/19 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 06/19 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN 07/12 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN 09/01 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 11/18 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 11/18 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 11/18 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16

depth (m) mgC/mgN 11/18 -200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN

12/04 first guess

-200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN

12/04 _{assimilated run}first guess

-200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN

-200 -150 -100 -50 0

0 2 4 6 8 10 12 14 16 mgC/mgN

Fig. 11. Mean carbon to nitrogen ratio profiles for year 1997 at DYFAMED. Thin dashed lines indicate that the algal biomass is very weak, and thus that the ratio is computed with very small values of C, Chl or N.

We also add two penalty terms toJ0. The first term,

Jp(k)=

1 2

p X

i=1

wi(ki−ki0)2,

accounts for the a priori parameter values and their standard deviations,σi = √1_w

i. This term forces the minimization to

avoid biologically absurd optimal parameter values. The second term,

Jrc(k)= wrc 2 X j X n

((12f (C/L)j,n−250)+)2,

where n refers to time and j to space, is added to pe-nalize carbon/chlorophyll ratio values greater than 250 mgC.mg Chla−1 which is considered as an upper bound by biologists. The choice of the weightwrc is not

straightfor-ward, since a compromise has to be found between the qual-ity of the minimization ofJ0and realistic bound for the

car-bon/chlorophyll ratios. In practice,wrc was chosen so that

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0 50 100 150 200 250 300

0 100 200 300 400 500 600 700 800

mgC/mgChl

Watt/m2

Fig. 12. Carbon to chlorophyll ratio versus light intensity. Mean values and standard deviation by interval of light intensity of length

10 Watt/m2 calculated for the whole water column during year

1997. The thin dashed line corresponds to the parameterization of this ratio as function of light given by Eqs. (27) and (28). The bold dashed line corresponds to the ratio obtained in Faugeras et al. (2003) plotted against the mean light intensity in the water column.

Table 4. Flux data (from Marty and Chiaverini, 2002) and com-puted fluxes at 200m with the Redfieldian NNPZD-DOM model

and the Mechanistic model. Values are given in gC.m−2.y−1. NU

stands for NO₃uptake, TP for total production, EF for export flux.

flux data Redfieldian

model

Mech. model first guess

Mech. model opt.

NU 42±15 49.6 48.7 47.2

TP 156±30 136.2 92.8 106.3

EF 2_±0.8 2.4 0.2 2.5

4 Numerical results

4.1 Model fit to the DYFAMED data

An a priori parameter set is constructed in the following way: parameters which were already included in the NNPZD-DOM model are given the values estimated using data from the DYFAMED station in Faugeras et al. (2003). Parameters coming from the BIOLOV model are given the values pro-posed in Pawlowski et al. (2002). A few parameters were then hand-tuned empirically in order to obtain a qualitatively correct first guess simulation. Note that since parameterKL

(Table 2) only enters the equations of the BIOLOV model in theαKLproduct form (Eq. 15), for the sake of parameter

estimation those two parameters are concatenated in a single parameterαK.

A first run is carried out using the a priori parameter set and without any data assimilation. Figures 7, 8 and 9 show surface chlorophyll, chlorophyll and nitrate profiles com-puted with the Mechanistic model versus the data (for the

0 0.5 1 1.5 2 2.5

0 100 200 300 400 500 600 700 800

mgChl/mmolN

Watt/m2

Fig. 13. Chlorophyll to nitrogen ratio versus light intensity. Mean values and standard deviation by interval of light intensity of length

10 Watt/m2computed for the whole water column during year 1997.

The dashed line corresponds to the parameterization of this ratio as function of light given by Eqs. (27) and (28).

sake of completeness the results given by the Redfieldian model with the light dependent C:Chl ratio described in Sec-tion 4.2 are also depicted on the same figures). The seasonal variability is well reproduced, but the spring bloom appears to be too strong and the transition towards oligotrophy poorly represented. This first guess run predicts reasonably good TP and NU fluxes estimates (Table 4). On the other hand, the export flux is underestimated and is associated with an underestimation of the zooplankton content (Table 5).

The evolution over time of the chlorophyll and nitrate data profiles (Figs. 8, 9) reflects the seasonal variability at DY-FAMED. Winter mixing brings nutrients to the surface, but the short residence time of algae in the euphotic layer, swept along by strong vertical motions, prevents the development of biomass. As the year progresses, the surface layer be-comes more stable, thus allowing the winter nutrient enrich-ment to be utilized continuously and finally allowing the al-gae bloom. From mid-May to November, the situation re-mains fairly stable with the upper layer nutrient content very low, and the system mainly oligotrophic and characterized by a deep chlorophyll maximum. It may be noticed that the nitrate profiles show strong variability below 100m. This variability cannot be attributed to biological processes since these occur closer to the surface, and it is therefore most likely due to horizontal advection. It cannot therefore be cap-tured by the model. During the oligotrophic period, the loca-tion of the nitracline and the deep chlorophyll maximum is fairly constant. This may be an indication of the absence of strong Ekman pumping and a crude justification for neglect-ing vertical advection.

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Table 5. Zooplankton content data and computed values at 200 m, with the Redfieldian NNPZD-DOM model and the Mechanistic

model, for May 1997, in mmolN m−2.

data Redfieldian

model

Mech. model first guess

Mech. model opt.

20±10 33.3 1.3 19.1

Table 6. Optimal adimensionalized (K/K0) parameters of the

Mechanistic model.

parameter optimal set

kopt

kn 0.944

γ 0.971

r 0.404

gz 1.314

kz 1.135

ap 0.855

ad 0.802

µz 1.220

mp 1.394

mz 0.850

µd 0.867

vd 0.347

τ 1.003

fn 0.947

µn 0.993

µdm 1.299

ρm 1.335

KI2 0.590

KC 0.740

α 1.218

αK 0.464

KI 1.041

λ 1.121

β 1.059

f 0.948

set, we did not include them in the control vector. The opti-mal parameter set is shown on Table 6.

The parameter estimation procedure resulted in several im-provements in the simulation. Bloom intensity is divided by a factor of two, in agreement with the observations (Fig. 7). Chlorophyll profiles during the bloom (dates 2 and 21 March on Fig. 8) also show a better fit with the data. The subsur-face chlorophyll maximum is well simulated in oligotrophic regime (dates 19 June, 12 July and 1 September). This re-sults from the use of a variable C:Chl ratio. Concerning NO3

profiles the improvement is less significant. This problem already occurred in former studies and was attributed to the fact that these profiles are affected by 3D physics not taken into account in the model. Data assimilation also forces the

Table 7. Total production computed at 200 m with the Redfieldian model and the Mechanistic model. “TP in C” is the flux computed

in carbon unit (gC.m−2.y−1) and “TP in N” is the flux computed in

nitrogen unit (gN.m−2.y−1).

flux Redfieldian model Mechanistic model

TP in C 136.2 106.3

TP in N 23.9 28.5

model to predict correct zooplankton quantities (Table 5) and correct fluxes estimates (Table 4). Concerning the total pro-duction flux (TP), it is worth to notice that if in the Redfiel-dian model it is computed in nitrogen unit and then converted to carbon unit using a constant C:N ratio, in the Mechanistic model this flux is directly computed in carbon unit through the formulation

T P ₌a(I )L₋λC (mmolC/m3/s).

This formulation can also lead to negative production values when respiration is stronger than photosynthesis. This situ-ation occurs at least every night in the model whena(I )₌0. Table 7 shows total production for both the mechanistic and the Redfieldian model computed in carbon unit or nitrogen unit. Total production in carbon unit is higher for the Red-fieldian model than for the Mechanistic model whereas the contrary holds for this flux computed in nitrogen unit. How-ever this difference cannot be considered as significant with regard to the uncertainty of the data. The same remark holds for the differences which appear in Figs. 7, 8 and 9 between the Mechanistic model and the Redfieldian model.

Figure 10 shows the C:Chl ratio profiles at the same dates than the Chl profiles of Fig. 8. The Mechanistic model sim-ulates values which are in accordance with what one should have expected. Globally the ratio decreases with depth that is to say with light. This is certainly a consequence of the BIOLOV model’s structure which was designed to simu-late these features observed experimentally at steady state (Pawlowski et al. (2002), Geider et al. (1998), Chalup and Laws (1990)). The bloom and post-bloom period corre-spond to relatively low C:Chl ratio values (lower than 100 mgC/mgChl) and relatively homogeneous profiles. On the contrary during summer when the oligotrophic regime occurs surface values are high (between 200 and 250 mgC/mgChl) and the ratio rapidly decreases with depth from 0 to about 50 m which corresponds to the depth of the subsurface chlorophyll maximum.

With the Mechanistic model the C:N ratio, computed as

(15)

-2e-05 0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 jan.

mmolC/m3/s

depth(m)

-2e-05 0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) feb.

-2e-05 0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) march

-2e-05 0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0

mmolC/m3/s

depth (m) april

-2e-05 0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) may

-2e-05 0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) june

-2e-06 0 2e-06 4e-06 6e-06 8e-06 1e-05 1.2e-05 1.4e-05

-200 -150 -100 -50 0

mmolC/m3/s

depth (m) july

-2e-06 0 2e-06 4e-06 6e-06 8e-06 1e-05 1.2e-05 1.4e-05

-200 -150 -100 -50 0 depth (m) august

-2e-06 0 2e-06 4e-06 6e-06 8e-06 1e-05 1.2e-05 1.4e-05

-200 -150 -100 -50 0 depth (m) sept.

-2e-06 0 2e-06 4e-06 6e-06 8e-06 1e-05 1.2e-05 1.4e-05

-200 -150 -100 -50 0

mmolC/m3/s

depth (m) oct.

-2e-06 0 2e-06 4e-06 6e-06 8e-06 1e-05 1.2e-05 1.4e-05

-200 -150 -100 -50 0 nov.

depth (m)

-2e-06 0 2e-06 4e-06 6e-06 8e-06 1e-05 1.2e-05 1.4e-05

-200 -150 -100 -50 0 depth (m) dec.

Fig. 14. Monthly total production profiles for the Mechanistic model.

even if the values reach sometimes too low thresholds proba-bly due to the higher carbon losses by respiration than nitro-gen losses in strong light limitation conditions. Table 8 gives the mean C:Chl and C:N ratios computed with the Mecha-nistic model. The low values reached by the C:N ratio lead to a mean value of this ratio lower than the classical Redfield ratio.

4.2 Variability of the predicted ratios

(16)

0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 jan.

mmolC/m3/s

depth (m)

0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) feb.

0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) march

0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0

mmolC/m3/s

depth (m) april

0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) may

0 2e-05 4e-05 6e-05 8e-05 0.0001

-200 -150 -100 -50 0 depth (m) june